[Grin] Sounds like you are enjoying the New Year. Well, for the question, let's specify that we are going to stay in the observer's frame of reference. From our point of view the steel ball is traveling several centimeters per second slower than light so we had better look quickly. As the ball approaches the observation horizon of the black hole it does not accelerate at the rate we expect. Strangely, the rate of acceleration slows down as it gets closer to c, the speed of light. At the same time, it seems to distort and a handy gravitational scanner that we are pointing at it shows an increase in mass. Somehow the energy of acceleration is being diverted into mass. The energy books stay balanced in our frame of reference but we suddenly are observing that factors we are used to thinking of as independent are really interrelated. One way to increase the energy of an object in motion is to increase its velocity; another way is to increase its mass. The time dilation effect does not matter to the observer in this case, though that is the one that people usually like to emphasize.

Graham --

Wouldn't we be getting into the realm of conversion of the mass to energy or of energy to mass at that point? Perhaps it might result in a big bang and create an entire universe?

Replying to Dave Bell. Ayup! The energy budget I am referring to is complicated. Some of the energy we expect to see added by acceleration is diverted into the apparent rest mass of the steel ball according to the E = mc squared rule. Some of it shows up as the Kinetic Energy of that additional mass traveling at near light speed. And the remainder causes a slight increase in velocity of the steel ball. I had to delete a sentence or two from my original answer because I seemed to be oversimplifying.

Oops, thanks for the post, but I guess I should have thought out my question more. I should have put a planet instead of blackhole, knowing what a blackhole can do to the universe =)

Here is my modified question:
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Ok a 1cm diameter steel ball is traveling at 1 mile an hour slower than the speed of light.

It approaches head-on the biggest planet you can imagine. Since objects accelerate by the pull of gravity, will it violate the law of relativity?

I trust this has been thought out, but I would like the full explanation as to why it would stop accelerating.
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I don't want to be anywhere near there when they meet don't care if its the energy released or the mas distroyed.
abr {h}